Tema15 - CHAPTER 15 15.1(Note Although it is not really...

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CHAPTER 15 15.1 (Note: Although it is not really clear from the problem statement, it should be assumed that each unit of product is equivalent to a kg.) ( a ) Define x a = amount of product A produced, and x b = amount of product B produced. The objective function is to maximize profit, P x x a b = + 45 30 Subject to the following constraints 20 5 10000 x x a b + {raw materials} 0 05 015 40 . . x x a b + {production time} x x a b + 550 {storage} x x a b , 0 {positivity} ( b ) To solve graphically, the constraints can be reformulated as the following straight lines x x b a = - 2000 4 {raw materials} x x b a = - 266 667 0 3333 . . {production time} x x b a = - 550 {storage} The objective function can be reformulated as x P x b a = - ( / ) . 1 30 15 The constraint lines can be plotted on the x b - x a plane to define the feasible space. Then the objective function line can be superimposed for various values of P until it reaches the boundary. The result is P 2245 23700 with x a 2245 483 and x b 2245 67. Notice also that material and storage are the binding constraints and that there is some slack in the time constraint.
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0 100 200 300 0 200 400 600 P = 1 5 0 2 3 7 x b x a t i m e s o r a g l optimum ( c ) The simplex tableau for the problem can be set up and solved as Basis P xa xb S1 S2 S3 Solution Intercept P 1 -45 -30 0 0 0 0 material S1 0 20 5 1 0 0 10000 500 time S2 0 0.05 0.15 0 1 0 40 800 storage S3 0 1 1 0 0 1 550 550 Basis P
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Tema15 - CHAPTER 15 15.1(Note Although it is not really...

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